Generation of One-Dimensional Probability Distributions Using Diffusion Processes

Computational project. Universidad de los Andes (2026)

This work implements a one-dimensional diffusion model that generates a bimodal distribution from noise. We show that the forward process is equivalent to a Langevin equation with a time-dependent coefficient, and that the neural network learns the score function, i.e., the restoring force that enables the diffusion process to be reversed. The model is validated by comparing the theoretical score of the target distribution with that estimated by the network at different time steps, showing excellent agreement, particularly at large times, where it approaches −x. Histograms of the generated samples overlap almost perfectly with the true distribution, demonstrating that the model reproduces the bimodality and captures the reverse Langevin dynamics. This one-dimensional prototype provides a testbed that can be scaled to high-dimensional problems.


Grupo de Física Estadística

Departamento de Física

Edificio Ip

Carrera 1E # 18A-10

Bogotá, Colombia

Universidad de los Andes | Vigilada Mineducación
Reconocimiento como Universidad: Decreto 1297 del 30 de mayo de 1964.
Reconocimiento personería jurídica: Resolución 28 del 23 de febrero de 1949 Minjusticia.

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